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INFLUENCE OF THE AIR HOLE’S DIAMETER ON OPTICAL PROPERTIES OF BK7-GLASS PHOTONIC CRYSTAL FIBER Chu Van Lanh1*, Vu Tran Quoc2, Dinh Xuan Khoa1, Nguyen Thi Hong Sang3, Thai Doan Thanh4, Doan Quoc Khoa5, Ho Quang Quy6 Abstract: In this paper, the configuration of BK7- glass photonic crystal fiber with a regular hexagonal lattice with air holes of different diameter and the field distribution of fundamental mode are simulated by Lumica - Mode Solutions. Some optical properties are numerically studied by finite element method and discussed. Keywords: Photonic crystal fibres, Fused glass, Effective refractive index, Group velosity, Dispersion.

I. INTRODUCTION The maximum transmission distance which can be achieved in modern optical communication is limited not only by the material properties (absorption and scattering) but also by the dispersion. Fortunately, the dielectric medium usually responds nonlinearly when stimulated by the intense wave and the trade-off between the dispersion and the nonlinear behaviour of the fibre can create localized structures (solitons) in space and/or time. These phenomena play an essential role in optical communication technology [1,2]. Therefore the dispersion engineering has been the subject of particular interest for a long time in optical fibres technology. Recently photonic crystal fibers (PCFs) attract a lot of attention due to several advantages over conventional optical fibers. PCF is a fibre with twodimensional cross-section structure in form of a photonic crystal. The structure usually consists of a central defect region surrounded by multiple air-holes. Since the PCFs discovery [3–5] a huge number of papers were published which changed many branches of optics. PCFs are now widely applied in fiber-optics, fiber lasers, light amplifiers, high-power transmission, highly sensitive gas sensors [6], nonlinear devices and other areas. One of the methods to engineer the dispersion properties of the PCFs is infiltrating the holes with some liquids [7–9]. By changing the size of the holes the optical propesties as effective refracrive index, group velocity and dispersion are changed corelatively. In the presented paper, we restrict ourselves to considering the PCF structure with 8 rings of air holes with a lattice constant of Λ=5 μm and hole’s diameter of (14)m. From these structures we study some optical properties of fundamental mode. II. OPTICAL PROPERTIES In our simulations, we considered fibers with regular hexagonal lattice and various hole diameters. We assume that PCFs manufacture from a fused silica of BK7 with air holes. The lattice constant was selected of 5m, firstly to ensure good coupling efficiency between standard single mode fibre and the considered PCF, and secondly to broaden the range of hole diameter (d) changing from 1m to 4m. The structure of analyzed hexagonal lattice PCFs with photonic crystal cladding with lattice constant =5m and air hole’s diameter d=(14)m and the relating intensity distribution of fundamental guided mode are simulated by

Tạp chí Nghiên cứu KH&CN quân sự, Số 44, 08 - 2016

99

Vật lý

Lumica-Mode Simulation (LMS) used in previous works [10, 14, 18] and presented in Figure 1.

Figure 1. The hexagonal lattice BK7-PCFs with air hole (upper) and relating intensity distribution of fundamental mode. From Figure 1 we can see an effect of the lattice, in which one ring of holes oprerates as one transmission holographic grating. For the given lattice constant, the width of slit in grating descreases with increasing of hole’s diameter (Figure 1:upper). According to Fraunhofer diffraction from a rectangular aperture [19], if width of slit decreases, the difraction angle increases and transmission intensity of first zero of pattern decreases. That leads the area of intensity of fundametal mode, ie. the first zero of pattern, in the core deacreses with increasing of hole diameter (Figure 1: downer) after difraction through 16 transmission holographic gratings. Following [2] the frequency dependence of the propagation constant ( ) is called dispersion and can be expressed by the following formula:

( ) n( )

c The ( ) can be expressed as a Taylor series about the carrier frequency 0

(1)

( ) 0 1 ( 0 ) 2 ( 0 ) 2 ...

(2)

d k ( ) , k 1, 2,... d k

(3)

where

k ( )

0

Here 1 is equal to the inverse of the group velocity vg . Together with the definition of 2 it leads to the relation:

2 ( )

d 1 d 1 1 dvg 2 d d vg vg d

(4)

The 2 is called the group velocity dispersion (GVD) and describes the change of group velocity with frequency. Here two dispersion regimes are considered. For 2 >0 (so-called normal dispersion regime) the longer waves travel faster than

100 C. V. Lanh, V. T. Quoc, …, “Influence of the air hole’s diameter… photonic crystal fiber.”

Nghiên cứu khoa học công nghệ

shorter ones. For 2

INFLUENCE OF THE AIR HOLE’S DIAMETER ON OPTICAL PROPERTIES OF BK7-GLASS PHOTONIC CRYSTAL FIBER Chu Van Lanh1*, Vu Tran Quoc2, Dinh Xuan Khoa1, Nguyen Thi Hong Sang3, Thai Doan Thanh4, Doan Quoc Khoa5, Ho Quang Quy6 Abstract: In this paper, the configuration of BK7- glass photonic crystal fiber with a regular hexagonal lattice with air holes of different diameter and the field distribution of fundamental mode are simulated by Lumica - Mode Solutions. Some optical properties are numerically studied by finite element method and discussed. Keywords: Photonic crystal fibres, Fused glass, Effective refractive index, Group velosity, Dispersion.

I. INTRODUCTION The maximum transmission distance which can be achieved in modern optical communication is limited not only by the material properties (absorption and scattering) but also by the dispersion. Fortunately, the dielectric medium usually responds nonlinearly when stimulated by the intense wave and the trade-off between the dispersion and the nonlinear behaviour of the fibre can create localized structures (solitons) in space and/or time. These phenomena play an essential role in optical communication technology [1,2]. Therefore the dispersion engineering has been the subject of particular interest for a long time in optical fibres technology. Recently photonic crystal fibers (PCFs) attract a lot of attention due to several advantages over conventional optical fibers. PCF is a fibre with twodimensional cross-section structure in form of a photonic crystal. The structure usually consists of a central defect region surrounded by multiple air-holes. Since the PCFs discovery [3–5] a huge number of papers were published which changed many branches of optics. PCFs are now widely applied in fiber-optics, fiber lasers, light amplifiers, high-power transmission, highly sensitive gas sensors [6], nonlinear devices and other areas. One of the methods to engineer the dispersion properties of the PCFs is infiltrating the holes with some liquids [7–9]. By changing the size of the holes the optical propesties as effective refracrive index, group velocity and dispersion are changed corelatively. In the presented paper, we restrict ourselves to considering the PCF structure with 8 rings of air holes with a lattice constant of Λ=5 μm and hole’s diameter of (14)m. From these structures we study some optical properties of fundamental mode. II. OPTICAL PROPERTIES In our simulations, we considered fibers with regular hexagonal lattice and various hole diameters. We assume that PCFs manufacture from a fused silica of BK7 with air holes. The lattice constant was selected of 5m, firstly to ensure good coupling efficiency between standard single mode fibre and the considered PCF, and secondly to broaden the range of hole diameter (d) changing from 1m to 4m. The structure of analyzed hexagonal lattice PCFs with photonic crystal cladding with lattice constant =5m and air hole’s diameter d=(14)m and the relating intensity distribution of fundamental guided mode are simulated by

Tạp chí Nghiên cứu KH&CN quân sự, Số 44, 08 - 2016

99

Vật lý

Lumica-Mode Simulation (LMS) used in previous works [10, 14, 18] and presented in Figure 1.

Figure 1. The hexagonal lattice BK7-PCFs with air hole (upper) and relating intensity distribution of fundamental mode. From Figure 1 we can see an effect of the lattice, in which one ring of holes oprerates as one transmission holographic grating. For the given lattice constant, the width of slit in grating descreases with increasing of hole’s diameter (Figure 1:upper). According to Fraunhofer diffraction from a rectangular aperture [19], if width of slit decreases, the difraction angle increases and transmission intensity of first zero of pattern decreases. That leads the area of intensity of fundametal mode, ie. the first zero of pattern, in the core deacreses with increasing of hole diameter (Figure 1: downer) after difraction through 16 transmission holographic gratings. Following [2] the frequency dependence of the propagation constant ( ) is called dispersion and can be expressed by the following formula:

( ) n( )

c The ( ) can be expressed as a Taylor series about the carrier frequency 0

(1)

( ) 0 1 ( 0 ) 2 ( 0 ) 2 ...

(2)

d k ( ) , k 1, 2,... d k

(3)

where

k ( )

0

Here 1 is equal to the inverse of the group velocity vg . Together with the definition of 2 it leads to the relation:

2 ( )

d 1 d 1 1 dvg 2 d d vg vg d

(4)

The 2 is called the group velocity dispersion (GVD) and describes the change of group velocity with frequency. Here two dispersion regimes are considered. For 2 >0 (so-called normal dispersion regime) the longer waves travel faster than

100 C. V. Lanh, V. T. Quoc, …, “Influence of the air hole’s diameter… photonic crystal fiber.”

Nghiên cứu khoa học công nghệ

shorter ones. For 2